Solve for $x$ and $y$ using elimination. $\begin{align*}-3x-5y &= 4 \\ 5x+3y &= -8\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $3$ and the bottom equation by $5$ $\begin{align*}-9x-15y &= 12\\ 25x+15y &= -40\end{align*}$ Add the top and bottom equations. $16x = -28$ Divide both sides by $16$ and reduce as necessary. $x = -\dfrac{7}{4}$ Substitute $-\dfrac{7}{4}$ for $x$ in the top equation. $-3( -\dfrac{7}{4})-5y = 4$ $\dfrac{21}{4}-5y = 4$ $-5y = -\dfrac{5}{4}$ $y = \dfrac{1}{4}$ The solution is $\enspace x = -\dfrac{7}{4}, \enspace y = \dfrac{1}{4}$.